Add to ORKGIn this note we show that the so-called weakly extensional arithmeticin all finite types, which is based on a quantifier-free rule ofextensionality due to C. Spector and which is of significance in thecontext of G¨odel's functional interpretation, does not satisfy the deductiontheorem for additional axioms. This holds already for PI^0_1-axioms. Previously, only the failure of the stronger deduction theoremfor deductions from (possibly open) assumptions (with parameterskept fixed) was known
AbstractIn 1981, Paris and Wilkie [J. Paris and A. Wilkie, “Δ0 Sets and Induction”, 1981 Jadswin Con...
AbstractIn [W. Burr, Functional interpretation of Aczel's constructive set theory, Annals of Pure an...
The paper investigates from a proof-theoretic perspective various non-contractive logical systems, w...
AbstractIt is shown that relative to intuitionistic arithmetic in all finite types extensionality an...
By a theorem of R. Kaye, J. Paris and C. Dimitracopoulos, the class of the ¦n+1–sentences true in t...
In [15],[16] Kreisel introduced the no-counterexample interpretation (n.c.i.) of Peanoarithmetic. In...
We prove that the standard cut is definable in each existentially closed model of IΔ0 + exp by a (pa...
The so-called weak K¨onig's lemma WKL asserts the existence of an infinitepath b in any infinite bin...
We show that the so-called weak Markov's principle (WMP) which states that every pseudo-positive rea...
We show that the types of the witnesses in the Herbrand functional interpretation can be simplified,...
The weak König's lemma WKL is of crucial significance in the study of fragments of mathematics which...
We can measure the complexity of a logical formula by counting the number of alternations between ex...
Recently, Coquand and Palmgren considered systems of intuitionistic arithmeticin all finite types to...
In this paper the numerical strength of fragments of arithmeticalcomprehension, choice and general u...
AbstractWe develop a quantifier-free logic for deriving consequences of multialgebraic theories. Mul...
AbstractIn 1981, Paris and Wilkie [J. Paris and A. Wilkie, “Δ0 Sets and Induction”, 1981 Jadswin Con...
AbstractIn [W. Burr, Functional interpretation of Aczel's constructive set theory, Annals of Pure an...
The paper investigates from a proof-theoretic perspective various non-contractive logical systems, w...
AbstractIt is shown that relative to intuitionistic arithmetic in all finite types extensionality an...
By a theorem of R. Kaye, J. Paris and C. Dimitracopoulos, the class of the ¦n+1–sentences true in t...
In [15],[16] Kreisel introduced the no-counterexample interpretation (n.c.i.) of Peanoarithmetic. In...
We prove that the standard cut is definable in each existentially closed model of IΔ0 + exp by a (pa...
The so-called weak K¨onig's lemma WKL asserts the existence of an infinitepath b in any infinite bin...
We show that the so-called weak Markov's principle (WMP) which states that every pseudo-positive rea...
We show that the types of the witnesses in the Herbrand functional interpretation can be simplified,...
The weak König's lemma WKL is of crucial significance in the study of fragments of mathematics which...
We can measure the complexity of a logical formula by counting the number of alternations between ex...
Recently, Coquand and Palmgren considered systems of intuitionistic arithmeticin all finite types to...
In this paper the numerical strength of fragments of arithmeticalcomprehension, choice and general u...
AbstractWe develop a quantifier-free logic for deriving consequences of multialgebraic theories. Mul...
AbstractIn 1981, Paris and Wilkie [J. Paris and A. Wilkie, “Δ0 Sets and Induction”, 1981 Jadswin Con...
AbstractIn [W. Burr, Functional interpretation of Aczel's constructive set theory, Annals of Pure an...
The paper investigates from a proof-theoretic perspective various non-contractive logical systems, w...