Some independence results in interpretability logic

Studia Logica ◽  
1991 ◽  
Vol 50 (1) ◽  
pp. 29-38 ◽  
Author(s):  
Vítězslav Švejdar
Keyword(s):  
Interpretability Logic ◽  
Independence Results

scholarly journals Several results on compact metrizable spaces in $$\mathbf {ZF}$$

2021 ◽  
Author(s):  
Kyriakos Keremedis ◽  
Eleftherios Tachtsis ◽  
Eliza Wajch
Keyword(s):  
Continuum Hypothesis ◽  
Compact Spaces ◽  
Power Set ◽  
Compact Metrizable Space ◽  
Permutation Models ◽  
Independence Results ◽  
The Axiom Of Choice ◽  
Metrizable Spaces ◽  
Transfer Theorems ◽  
The Continuum

AbstractIn the absence of the axiom of choice, the set-theoretic status of many natural statements about metrizable compact spaces is investigated. Some of the statements are provable in $$\mathbf {ZF}$$ ZF , some are shown to be independent of $$\mathbf {ZF}$$ ZF . For independence results, distinct models of $$\mathbf {ZF}$$ ZF and permutation models of $$\mathbf {ZFA}$$ ZFA with transfer theorems of Pincus are applied. New symmetric models of $$\mathbf {ZF}$$ ZF are constructed in each of which the power set of $$\mathbb {R}$$ R is well-orderable, the Continuum Hypothesis is satisfied but a denumerable family of non-empty finite sets can fail to have a choice function, and a compact metrizable space need not be embeddable into the Tychonoff cube $$[0, 1]^{\mathbb {R}}$$ [ 0 , 1 ] R .

scholarly journals Independence of algebraic monodromy groups in compatible systems

2021 ◽  
Vol 27 (4) ◽  
Author(s):  
Federico Amadio Guidi
Keyword(s):  
Galois Representations ◽  
Global Function ◽  
Irreducible Decomposition ◽  
Global Function Fields ◽  
Normal Varieties ◽  
Independence Result ◽  
Monodromy Groups ◽  
Independence Results ◽  
Lisse Sheaves ◽  
General Method

AbstractIn this paper we develop a general method to prove independence of algebraic monodromy groups in compatible systems of representations, and we apply it to deduce independence results for compatible systems both in automorphic and in positive characteristic settings. In the abstract case, we prove an independence result for compatible systems of Lie-irreducible representations, from which we deduce an independence result for compatible systems admitting what we call a Lie-irreducible decomposition. In the case of geometric compatible systems of Galois representations arising from certain classes of automorphic forms, we prove the existence of a Lie-irreducible decomposition. From this we deduce an independence result. We conclude with the case of compatible systems of Galois representations over global function fields, for which we prove the existence of a Lie-irreducible decomposition, and we deduce an independence result. From this we also deduce an independence result for compatible systems of lisse sheaves on normal varieties over finite fields.

Algebraic Independence Results Related to 〈q, r〉-Number Systems

2006 ◽  
Vol 147 (4) ◽  
pp. 319-335 ◽  
Author(s):  
Shin-ichiro Okada ◽  
Iekata Shiokawa
Keyword(s):  
Algebraic Independence ◽  
Number Systems ◽  
Independence Results

scholarly journals Interpretability over peano arithmetic

1999 ◽  
Vol 64 (4) ◽  
pp. 1407-1425
Author(s):  
Claes Strannegård
Keyword(s):  
Modal Logic ◽  
Completeness Theorem ◽  
Peano Arithmetic ◽  
Embedding Theorem ◽  
Compactness Theorem ◽  
Partial Answer ◽  
Recursively Enumerable ◽  
Recursively Enumerable Sets ◽  
Interpretability Logic

AbstractWe investigate the modal logic of interpretability over Peano arithmetic. Our main result is a compactness theorem that extends the arithmetical completeness theorem for the interpretability logic ILMω. This extension concerns recursively enumerable sets of formulas of interpretability logic (rather than single formulas). As corollaries we obtain a uniform arithmetical completeness theorem for the interpretability logic ILM and a partial answer to a question of Orey from 1961. After some simplifications, we also obtain Shavrukov's embedding theorem for Magari algebras (a.k.a. diagonalizable algebras).

scholarly journals A note on the interpretability logic of finitely axiomatized theories

Studia Logica ◽  
1991 ◽  
Vol 50 (2) ◽  
pp. 241-250 ◽  
Author(s):  
Maarten de Rijke
Keyword(s):  
Interpretability Logic

Field Independence and Resistance to Reversal of Perspective

1966 ◽  
Vol 22 (2) ◽  
pp. 543-546 ◽  
Author(s):  
Frank Haronian ◽  
A. Arthur Sugerman
Keyword(s):  
Short Form ◽  
Necker Cube ◽  
Normal Male ◽  
Field Independence ◽  
Embedded Figures Test ◽  
Following Instructions ◽  
Independence Results ◽  
Male University Students ◽  
Rod And Frame Test ◽  
Rod And Frame

The more successful 102 normal male university students were in following instructions to resist fluctuations of the Necker cube, the more field-independently they scored on both Series III of the rod-and-frame test ( r = .28) and on Jackson's short form of the embedded-figures test ( r = .24). Under neutral instructions, the correlations were nil. Results support prior findings that a small but significant portion of the variance of Necker cube fluctuations under instructions to control the rate of shift is related to scores of field independence. Results support Jackson's finding that ability to control the rate of shift is not related to intelligence.

Reversion of Cancer Cells From Methionine-Addiction to Methionine Independence Results in Loss of Histone Lysine Overmethylation and Malignancy

2021 ◽  
Author(s):  
Jun Yamamoto ◽  
Sachiko Inubushi ◽  
Qinghong Han ◽  
Yoshihiko Tashiro ◽  
Norihiko Sugisawa ◽  
...  
Keyword(s):  
Cancer Cells ◽  
Histone Lysine ◽  
Independence Results
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