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Authors:KOSSAK; ROMAN, WCISŁO, BARTOSZ Pages: 231 - 253 Abstract: We introduce a tool for analysing models of , the compositional truth theory over Peano Arithmetic. We present a new proof of Lachlan’s theorem that the arithmetical part of models of are recursively saturated. We also use this tool to provide a new proof of theorem from [8] that all models of carry a partial inductive truth predicate. Finally, we construct a partial truth predicate defined for a set of formulae whose syntactic depth forms a nonstandard cut which cannot be extended to a full truth predicate satisfying . PubDate: 2021-01-05 DOI: 10.1017/bsl.2019.55
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Authors:SARGSYAN; GRIGOR, TRANG, NAM Pages: 254 - 266 Abstract: A set of reals is universally Baire if all of its continuous preimages in topological spaces have the Baire property. is a type of generic absoluteness condition introduced by Woodin that asserts in strong terms that the theory of the universally Baire sets cannot be changed by set forcings. The () is a determinacy axiom isolated by Woodin. It asserts that the largest Suslin cardinal is inaccessible for ordinal definable surjections. Let -- be the statement that in all (set) generic extensions there is a model of whose Suslin, co-Suslin sets are the universally Baire sets. We outline the proof that over some mild large cardinal theory, is equiconsistent with --. In fact, we isolate an exact theory (in the hierarchy of strategy mice) that is equiconsistent with both (see Definition 3.1). As a consequence, we obtain that is weaker than the theory “ PubDate: 2021-07-02 DOI: 10.1017/bsl.2021.29
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Authors:LETHEN; TIM Pages: 267 - 297 Abstract: This paper presents hitherto unpublished writings of Kurt Gödel concerning logical, epistemological, theological, and physical antinomies, which he generally considered as “the most interesting facts in modern logic,” and which he used as a basis for his famous metamathematical results. After investigating different perspectives on the notion of the logical structure of the antinomies and presenting two “antinomies of the intensional,” a new kind of paradox closely related to Gödel’s ontological proof for the existence of God is introduced and completed by a compilation of further theological antinomies. Finally, after a presentation of unpublished general philosophical remarks concerning the antinomies, Gödel’s type-theoretic variant of Leibniz’ Monadology, discovered in his notes on the foundations of quantum mechanics, is examined. Most of the material presented here has been transcribed from the Gabelsberger shorthand system for the first time. PubDate: 2021-07-26 DOI: 10.1017/bsl.2021.41
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, the compositional truth theory over Peano Arithmetic. We present a new proof of Lachlan’s theorem that the arithmetical part of models of 
are recursively saturated. We also use this tool to provide a new proof of theorem from [8] that all models of 
carry a partial inductive truth predicate. Finally, we construct a partial truth predicate defined for a set of formulae whose syntactic depth forms a nonstandard cut which cannot be extended to a full truth predicate satisfying 
.
is a type of generic absoluteness condition introduced by Woodin that asserts in strong terms that the theory of the universally Baire sets cannot be changed by set forcings. The 
(
) is a determinacy axiom isolated by Woodin. It asserts that the largest Suslin cardinal is inaccessible for ordinal definable surjections. Let 
-
-
be the statement that in all (set) generic extensions there is a model of 
whose Suslin, co-Suslin sets are the universally Baire sets. We outline the proof that over some mild large cardinal theory, 
is equiconsistent with 
-
-
. In fact, we isolate an exact theory (in the hierarchy of strategy mice) that is equiconsistent with both (see Definition 3.1). As a consequence, we obtain that 
is weaker than the theory “
