Bartosz Wcisło’s research while affiliated with University of Gdańsk and other places

... In [17], a proof has been presented that the principles PropSnd together with an axiom stating that for the quantifier-free formulae, truth predicate agrees with the canonical arithmetical truth predicate for ∆ 0 -formulae, becomes a nonconservative extension of PA (an alternative proof was found by Cieśliński and published in [3]). This result has already showed that PropSnd has surprising amount of strength and put several limitations on the hypothetical conservativeness proofs. ...

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Saturation properties for compositional truth with propositional correctness

... For technical convenience, the discussion below will be formulated in the language of satisfaction classes rather than truth predicates, as discussed in [12]. We are inclined to say that the definition used there is standard. ...

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Classical determinate truth without induction

... The recent work of Cieśliński, Łełyk, and Wcisło [7] refined the aforementioned work of Pakhomov and the author by showing that CT -[PA] + DC out is an axiomatization of CT 0 [PA], where DC out is the 'half' of DC that says every true disjunction has a true disjunct. In summary, the arithmetical strength of CT -[PA] augmented with seemingly innocuous axioms such as "truth is closed propositional proofs" or even "If a disjunction is true, then it has a true disjunct" goes beyond PA. 2 The philosophical ramifications of the nonconservativity of CT -[PA] + DC has been explored by Fujimoto [14], whose work shows that the nonconservativity of CT -[PA] + DC over PA introduces a new twist to the conservativity argument in relation to the deflationist conception of truth. ...

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SATISFACTION CLASSES WITH APPROXIMATE DISJUNCTIVE CORRECTNESS

... In the formulation of this condition, we will make use of an admittedly technical notion of syntactic similarity. Both this notion and its variants were introduced and discussed in [9], [11], and [12] together with examples which might be helpful for the reader. ...

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Classical determinate truth without induction

... Remark 3.6. In answer to a question of the author, Lawrence Wong noted that Wciłso's proof of Lachlan's theorem (as presented in [21]) shows that if M is a model of PA that has an expansion to a Form M -truth class, then M is recursively saturated. , presented both in [9,21], which refine the model-theoretic construction given in [12] for PA formulated in a relational language. ...

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SATISFACTION CLASSES WITH APPROXIMATE DISJUNCTIVE CORRECTNESS

... Here CTis a finitely axiomatized theory formulated in the language of arithmetic augmented with a truth predicate T (the minus superscript indicates that no instances of the induction scheme mentioning T have been added to the theory). Decades later, a new versatile model-theoretic method of constructing full satisfaction classes was presented by Visser and the author [12]; this new method has been refined in various directions, e.g., as in Cieśliński's monograph [4], and in the joint work of Łełyk and Wcisło with the author [9]. The conservativity of CT -[PA] over PA has also been established by proof theoretic methods by Leigh [25], and more recently by Cieśliński [5]. ...

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SATISFACTION CLASSES WITH APPROXIMATE DISJUNCTIVE CORRECTNESS

... In particular TCut is conservative over I 0 + exp. In [11] it is shown that TCut is mutually definable with a theory WPT − , which is a compositional theory of truth which compositional axioms are modelled after the Weak Kleene Logic. ...

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Varieties of truth definitions

... Another basic property of satisfaction classes is satisfying internal induction. Before introducing it let us define one handy abbreviation: if (M, S) |= CS − , and ψ is a formula in the sense of M with exactly one free variable, then T * ψ(x) denotes a L PA ∪ {S}-formula with one free variable x which naturaly expresses "The result of substituting the numeral naming x for the unique free variable of ψ is satisfied by the empty assignment"(see [8], Lemma 3.6.) We say that in (M, S) |= CS − , S satisfies the internal induction iff for every ψ ∈ Form M with a unique free variable, the formula T * ψ(x) satisfies the induction axiom, i.e. ...

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Pathologies in satisfaction classes

... The presence of truth in induction means that (PA U ) * ω does not, in general, admit cut elimination. 25 However, a result of Łełyk and Wcisło (2017) shows that PA T interprets (PA U ) ω , whence the conservativity of (PA U ) * ω over PA follows from Theorem 1. ...

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Components of arithmetic theory acceptance

... One example is the principle of propositional correctness which states that if a sentence φ follows in propositional logic from the set of premises Γ such that T (ψ) holds for all ψ ∈ Γ, then T (φ) holds. It turned out that this principle is equivalent to CT 0 , compositional truth with ∆ 0 -induction for the whole language (including the formulae with the truth predicate) which was shown in [14] to be nonconservative over PA. ...

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Saturation properties for compositional truth with propositional correctness