Antonio Montalbán, Indecomposable linear orderings and hyperarithmetic analysis. Journal of Mathematical Logic, vol. 6 (2006), no. 1, pp. 89–120. - Itay Neeman, The strength of Jullien’s indecomposability theorem. Journal of Mathematical Logic, vol. 8 (2008), no. 1, pp. 93–119. - Itay Neeman, Necessary use ofinduction in a reversal. Journal of Symbolic Logic, vol. 76 (2011), no. 2, pp. 561–574.

2014 ◽  
Vol 20 (3) ◽  
pp. 366-368
Author(s):  
Henry Towsner
Keyword(s):  
Mathematical Logic ◽  
Symbolic Logic ◽  
Linear Orderings

S. S. Goncharov. Autostability and computable families of constructivizations. Algebra and Logic, vol. 14 (1975), no. 6, pp. 392–409. - S. S. Goncharov. The quantity of nonautoequivalent constructivizations. Algebra and Logic, vol. 16 (1977), no. 3, pp. 169–185. - S. S. Goncharov and V. D. Dzgoev. Autostability of models. Algebra and Logic, vol. 19 (1980), no. 1, pp. 28–37. - J. B. Remmel. Recursively categorical linear orderings. Proceedings of the American Mathematical Society, vol. 83 (1981), no. 2, pp. 387–391. - Terrence Millar. Recursive categoricity and persistence. The Journal of Symbolic Logic, vol. 51 (1986), no. 2, pp. 430–434. - Peter Cholak, Segey Goncharov, Bakhadyr Khoussainov and Richard A. Shore. Computably categorical structures and expansions by constants. The Journal of Symbolic Logic, vol. 64 (1999), no. 1, pp. 13–137. - Peter Cholak, Richard A. Shore and Reed Solomon. A computably stable structure with no Scott family of finitary formulas. Archive for Mathematical Logic, vol. 45 (2006), no. 5, pp. 519–538. - Chris Ash, Julia Knight, Mark Manasse and Theodore Slaman. Generic copies of countable structures. Annals of Pure and Applied Logic, vol. 42 (1989), no. 3, pp. 195–205. - John Chisholm. Effective model theory vs. recursive model theory. The Journal of Symbolic Logic, vol. 55 (1990), no. 3, pp. 1168–1191.

2012 ◽  
Vol 18 (1) ◽  
pp. 131-134
Author(s):  
Daniel Turetsky
Keyword(s):  
Mathematical Logic ◽  
Model Theory ◽  
American Mathematical Society ◽  
Effective Model ◽  
Mathematical Society ◽  
Symbolic Logic ◽  
Applied Logic ◽  
Recursive Model ◽  
Linear Orderings ◽  
Scott Family

scholarly journals Relative Necessity and Propositional Quantification

2019 ◽  
Vol 49 (4) ◽  
pp. 703-726
Author(s):  
Alexander Roberts
Keyword(s):  
Mathematical Logic ◽  
Propositional Logic ◽  
Recent Article ◽  
Symbolic Logic ◽  
Philosophical Logic ◽  
Alternative Account ◽  
Standard Account ◽  
Current Article ◽  
Modal Propositional Logic ◽  
Propositional Quantification

AbstractFollowing Smiley’s (The Journal of Symbolic Logic, 28, 113–134 1963) influential proposal, it has become standard practice to characterise notions of relative necessity in terms of simple strict conditionals. However, Humberstone (Reports on Mathematical Logic, 13, 33–42 1981) and others have highlighted various flaws with Smiley’s now standard account of relative necessity. In their recent article, Hale and Leech (Journal of Philosophical Logic, 46, 1–26 2017) propose a novel account of relative necessity designed to overcome the problems facing the standard account. Nevertheless, the current article argues that Hale & Leech’s account suffers from its own defects, some of which Hale & Leech are aware of but underplay. To supplement this criticism, the article offers an alternative account of relative necessity which overcomes these defects. This alternative account is developed in a quantified modal propositional logic and is shown model-theoretically to meet several desiderata of an account of relative necessity.

Completeness Before Post: Bernays, Hilbert, and the Development of Propositional Logic

1999 ◽  
Vol 5 (3) ◽  
pp. 331-366 ◽  
Author(s):  
Richard Zach
Keyword(s):  
Mathematical Logic ◽  
Propositional Logic ◽  
Historical Context ◽  
Subsequent Development ◽  
Symbolic Logic ◽  
David Hilbert ◽  
Semantic Completeness ◽  
Lecture Notes ◽  
Truth Value

AbstractSome of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917–1923. The aim of this paper is to describe these results, focussing primarily on propositional logic, and to put them in their historical context. It is argued that truth-value semantics, syntactic (“Post-”) and semantic completeness, decidability, and other results were first obtained by Hilbert and Bernays in 1918, and that Bernays's role in their discovery and the subsequent development of mathematical logic is much greater than has so far been acknowledged.

R. Dalbiez. L'idée fondamentale de la combinatoire leibnizienne. Travaux du IXe Congrès International de Philosophie, VI Logique et mathématiques, Actualités scientifiques et industrielles 535, Hermann et Cie, Paris1937, pp. 3–7. - Thomas Greenwood. L'extension de la logique aristotélicienne. Travaux du IXe Congrès International de Philosophie, VI Logique et mathématiques, Actualités scientifiques et industrielles 535, Hermann et Cie, Paris1937, pp. 18–25. - Z. Zawtrski. Importance des recherches logiques et sémantiques pour les théories de la physique contemporaine. Travaux du IXe Congrès International de Philosophie, VI Logique et mathématiques, Actualités scientifiques et industrielles 535, Hermann et Cie, Paris1937, pp. 82–87. - Paulette Février. Les relations d'incertitude d'Heisenberg et la logique. Travaux du IXe Congrès International de Philosophie, VI Logique et mathématiques, Actualités scientifiques et industrielles 535, Hermann et Cie, Paris1937, pp. 88–94. [Cf. II 88.] - R. Catesby Taliaferro. Plato and the liberal arts: a plea for mathematical logic. The new scholasticism, vol. 11 (1937), pp. 297–319. - Arnold F. Emch. Deducibility with respect to necessary and impossible propositions. The journal of symbolic logic, vol. 2 (1937), pp. 78–81. - Garrett Birkhoff. Rings of sets. Duke mathematical journal, vol. 3 (1937), pp. 443–454. - N. H. McCoy and Deane Montgomery. A representation of generalized Boolean rings. Duke mathematical journal, vol. 3 (1937), pp. 455–459. - Gottfried Köthe. Die Theorie der Verbände, ein neuer Versuch zur Grundlegung der Algebra und der projektiven Geometrie. Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. 47 (1937), 1. Abteilung, pp. 125–144. - Adolf Fraenkel. Review of Carnap's Logische Syntax der Sprache (35212). Scripta mathematica, vol. 4 (1936), pp. 309–312. - A. P. Ushenko. Review of Carnap's The logical syntax of language. The philosophical review, vol. 46 (1937), pp. 549–553. - L. G. Review of Waismann's Einführung in das mathematische Denken (II 142). Rivista di filosofia, vol. 28 (1937), pp. 283–285. - Wilhelm Ackermann. Review of Bentley's Linguistic analysis of mathematics (4611). Jahrbuch über die Fortschritte der Mathematik, vol. 58I no. 1 (for 1932, pub. 1937), pp. 56–57. - C. G. Hempel. Review of Carnap's Die Antinomien und die Unvollständigkeit der Mathematik (35214). Jahrbuch über die Fortschritte der Mathematik, vol. 60II no. 1 (for 1934, pub. 1936), pp. 843–844. - Wilhelm Ackermann. Review of Quine's A system of logistic (4585). Jahrbuch über die Fortschritte der Mathematik, vol. 60II no. 1 (for 1934, pub. 1936), pp. 845–846. - C. G. Hempel. Review of Quine's Toward a calculus of concepts (I 111). Jahrbuch über die Fortschritte der Mathematik, vol. 62I no. 1 (1936), pp. 35–36. - Th. Skolem. Review of Tarski's Grundzüge des Systemenkalküls (28518, I 71). Jahrbuch über die Fortschritte der Mathematik, vol. 62I no. 1 (1936), pp. 38–39. - Friedrich Bachmann. Reviews of Gentzen's Die Widerspruchsfreiheit der Stufenlogik (I 119) and Die Widerspruchsfreiheit der reinen Zahlentheorie (I 75). Jahrbuch über die Fortschritte der Mathematik, vol. 62I no. 1 (1936), pp. 43–44. - M. Kokoszyńska. Filozofia nauki w Kole Wiedeńskim (Philosophy of science in the Circle of Vienna). Kwartalnik filozoficzny, vol. 13, pp. 151–165, 181–194. - M. Kokoszyńska. Review of Carnap's Testability and meaning (II 49). Kwartalnik filozoficzny, vol. 14, pp. 55–61. - M. Black. Review of Gonseth's Les mathématiques et la réalité (II 45). Mind, n.s. vol. 46 (1937), pp. 538–539. - Review of Carnap's Testability and meaning, part 2 (II 49). Mind, n.s. vol. 46 (1937), p. 546. - Edward Gleason Spaulding. A world of chance, or Whence, whither, and why. The Macmillan Company, New York, 1936, xxxiii+293 pp. - R. Feys. Notions de logistique. Mimeographed. 1st. edn., privately circulated, Brussels 1936, vi+102 pp. 2nd. edn., revised, on sale by the Revue Néoscolastique, Louvain 1937.

1937 ◽  
Vol 2 (4) ◽  
pp. 175-176
Keyword(s):  
New York ◽  
Mathematical Logic ◽  
Philosophy Of Science ◽  
Liberal Arts ◽  
Linguistic Analysis ◽  
Mathematical Journal ◽  
Symbolic Logic ◽  
Duke Mathematical Journal ◽  
Logical Syntax ◽  
Boolean Rings

Closing the Circle: An Analysis of Emil Post's Early Work

2006 ◽  
Vol 12 (2) ◽  
pp. 267-289 ◽  
Author(s):  
Liesbeth de Mol
Keyword(s):  
Mathematical Logic ◽  
Decision Problem ◽  
Symbolic Logic ◽  
Negative Solution ◽  
Kurt Gödel ◽  
Historical Fact

AbstractIn 1931 Kurt Gödel published his incompleteness results, and some years later Church and Turing showed that the decision problem for certain systems of symbolic logic has a negative solution. However, already in 1921 the young logician Emil Post worked on similar problems which resulted in what he called an “anticipation” of these results. For several reasons though he did not submit these results to a journal until 1941. This failure ‘to be the first’, did not discourage him: his contributions to mathematical logic and its foundations should not be underestimated. It is the purpose of this article to show that an interest in the early work of Emil Post should be motivated not only by this historical fact, but also by the fact that Post's approach and method differs substantially from those offered by Gödel, Turing and Church. In this paper it will be shown how this method evolved in his early work and how it finally led him to his results.

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