 Subjects -> PHILOSOPHY (Total: 762 journals)
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- BSL volume 28 issue 3 Cover and Front matter
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Pages: 1 - 3
PubDate: 2022-10-21
DOI: 10.1017/bsl.2022.31
- BSL volume 28 issue 3 Cover and Back matter
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Pages: 1 - 2
PubDate: 2022-10-21
DOI: 10.1017/bsl.2022.32
- AFFINE LOGIC FOR CONSTRUCTIVE MATHEMATICS
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Authors: SHULMAN; MICHAEL
Pages: 327 - 386
Abstract: We show that numerous distinctive concepts of constructive mathematics arise automatically from an “antithesis” translation of affine logic into intuitionistic logic via a Chu/Dialectica construction. This includes apartness relations, complemented subsets, anti-subgroups and anti-ideals, strict and non-strict order pairs, cut-valued metrics, and apartness spaces. We also explain the constructive bifurcation of some classical concepts using the choice between multiplicative and additive affine connectives. Affine logic and the antithesis construction thus systematically “constructivize” classical definitions, handling the resulting bookkeeping automatically.
PubDate: 2022-07-21
DOI: 10.1017/bsl.2022.28
- UNIVERSAL CODING AND PREDICTION ON ERGODIC RANDOM POINTS
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Authors: DĘBOWSKI; ŁUKASZ, STEIFER, TOMASZ
Pages: 387 - 412
Abstract: Suppose that we have a method which estimates the conditional probabilities of some unknown stochastic source and we use it to guess which of the outcomes will happen. We want to make a correct guess as often as it is possible. What estimators are good for this' In this work, we consider estimators given by a familiar notion of universal coding for stationary ergodic measures, while working in the framework of algorithmic randomness, i.e., we are particularly interested in prediction of Martin-Löf random points. We outline the general theory and exhibit some counterexamples. Completing a result of Ryabko from 2009 we also show that universal probability measure in the sense of universal coding induces a universal predictor in the prequential sense. Surprisingly, this implication holds true provided the universal measure does not ascribe too low conditional probabilities to individual symbols. As an example, we show that the Prediction by Partial Matching (PPM) measure satisfies this requirement with a large reserve.
PubDate: 2022-05-02
DOI: 10.1017/bsl.2022.18
- THE COLLAPSE OF THE HILBERT PROGRAM: A VARIATION ON THE GÖDELIAN
THEME
- AN AXIOMATIC APPROACH TO FORCING IN A GENERAL SETTING
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Authors: FREIRE; RODRIGO A., HOLY, PETER
Pages: 427 - 450
Abstract: The technique of forcing is almost ubiquitous in set theory, and it seems to be based on technicalities like the concepts of genericity, forcing names and their evaluations, and on the recursively defined forcing predicates, the definition of which is particularly intricate for the basic case of atomic first order formulas. In his [3], the first author has provided an axiomatic framework for set forcing over models of  that is a collection of guiding principles for extensions over which one still has control from the ground model, and has shown that these axiomatics necessarily lead to the usual concepts of genericity and of forcing extensions, and also that one can infer from them the usual recursive definition of forcing predicates. In this paper, we present a more general such approach, covering both class forcing and set forcing, over various base theories, and we provide additional details regarding the formal setting that was outlined in [3].
PubDate: 2022-04-04
DOI: 10.1017/bsl.2022.15
- A NOTE ON FRAGMENTS OF UNIFORM REFLECTION IN SECOND ORDER ARITHMETIC
- 2022 WINTER MEETING OF THE ASSOCIATION FOR SYMBOLIC LOGIC WITH THE AMS
Seattle, Washington Joint Mathematics Meeting January 7–8, 2022-
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Pages: 466 - 466
PubDate: 2022-10-21
DOI: 10.1017/bsl.2022.25
- 2022 WINTER MEETING OF THE ASSOCIATION FOR SYMBOLIC LOGIC WITH THE APA
Palmer House, Chicago, IL Central APA Meeting February 24, 2022-
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Pages: 467 - 469
PubDate: 2022-10-21
DOI: 10.1017/bsl.2022.26
- NOTICES
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Pages: 470 - 475
PubDate: 2022-10-21
DOI: 10.1017/bsl.2022.30
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, or something arbitrary if there is none. The Hilbertians claimed that in any proof in a number-theoretic system S, each ε-term can be replaced by a numeral, making each line provable and true. This implies that S must not only be consistent, but also 1-consistent (
-correct). Here we show that if the result is supposed to be provable within S, a statement about all 
statements that subsumes itself within its own scope must be provable, yielding a contradiction. The result resembles Gödel’s but arises naturally out of the Hilbert program itself.
extending 
and axiomatizable by a 
sentence, and for any 
, 
where T is 
augmented with full induction, and 
denotes the schema of transfinite induction up to 
for 
formulas without set parameters.
