The Baire category theoremover a feasible base theory

Boron oxide in the Na2O.P2O5-x B2O3 system behaves as a Lux base. Its addition to Na2O.P2O5 brings about transformation of a Co(II) indicator from octahedral to tetrahedral configuration, increase in the optical basicity ΛPb(II), increase in the relative basicity of the melt as determined by means of a galvanic cell, and depolymerization reactions releasing PO43- ions. In the Na2O-B2O3 system free of P2O5, boron oxide behaves as a Lux acid. The amphoretic nature of B2O3 is explained in terms of Lux's acid-base theory extended in analogy with the protolysis theory. The theoretical optical basicity values do not indicate the amphoretic behaviour of B2O3 because in this approach boron oxide is a priori regarded as more acidic than Na2O.P2O5.

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NOTES ON BOUNDED INDUCTION FOR THE COMPOSITIONAL TRUTH PREDICATE

The Review of Symbolic Logic ◽

10.1017/s1755020316000368 ◽

2017 ◽

Vol 10 (3) ◽

pp. 455-480 ◽

Cited By ~ 3

Author(s):

BARTOSZ WCISŁO ◽

MATEUSZ ŁEŁYK

Keyword(s):

Reflection Principle ◽

Peano Arithmetic ◽

Truth Predicate ◽

Base Theory ◽

Modified Theory ◽

Induction Scheme

AbstractWe prove that the theory of the extensional compositional truth predicate for the language of arithmetic with Δ0-induction scheme for the truth predicate and the full arithmetical induction scheme is not conservative over Peano Arithmetic. In addition, we show that a slightly modified theory of truth actually proves the global reflection principle over the base theory.

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Weaker cousins of Ramsey's theorem over a weak base theory

Annals of Pure and Applied Logic ◽

10.1016/j.apal.2021.103028 ◽

2021 ◽

pp. 103028

Author(s):

Marta Fiori-Carones ◽

Leszek Aleksander Kołodziejczyk ◽

Katarzyna W. Kowalik

Keyword(s):

Weak Base ◽

Ramsey's Theorem ◽

Base Theory ◽

Ramsey’S Theorem

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Stable Analysis of Solution Set for System of Quasivariational Relations with Applications

Journal of Applied Mathematics ◽

10.1155/2014/109616 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7

Author(s):

Lefeng Shi ◽

Zhe Yang

Keyword(s):

Baire Category ◽

Solution Set ◽

Stability Of Solutions ◽

Essential Component ◽

Essential Stability ◽

Essential Components ◽

Quasivariational Inclusions

The essential stability of solutions for system of quasivariational relations is studied. We show that most of systems of quasivariational relations are essential (in the sense of Baire category) and that, for any system of quasivariational relations, there exists at least one essential component of its solution set. As applications, the existence of essential components of solution set for systems of KKM problems and systems of quasivariational inclusions is obtained.

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Gröbner–Shirshov bases method for Gelfand–Dorfman–Novikov algebras

Journal of Algebra and Its Applications ◽

10.1142/s0219498817500013 ◽

2017 ◽

Vol 16 (01) ◽

pp. 1750001 ◽

Cited By ~ 6

Author(s):

L. A. Bokut ◽

Yuqun Chen ◽

Zerui Zhang

Keyword(s):

Word Problem ◽

Type Theorem ◽

Novikov Algebra ◽

Base Theory ◽

Novikov Algebras

We establish Gröbner–Shirshov base theory for Gelfand–Dorfman–Novikov algebras over a field of characteristic [Formula: see text]. As applications, a PBW type theorem in Shirshov form is given and we provide an algorithm for solving the word problem of Gelfand–Dorfman–Novikov algebras with finite homogeneous relations. We also construct a subalgebra of one generated free Gelfand–Dorfman–Novikov algebra which is not free.

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