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We prove the theorem from the title which answers a question addressed in the paper of Moore-Hrusak-Dzamonja .
Let H be a proof system for quantified propositional calculus (QPC). We define the Σ
-witnessing problem for H to be: given a prenex Σ
-formula A, an H-proof of A, and a truth assignment to the free variables in A, find a witness for the outermost existential quantifiers in A. We...
Axiomatic set theory with full comprehension is known to be consistent in Łukasiewicz fuzzy predicate logic. But we cannot assume the existence of natural numbers satisfying a simple schema of induction; this extension is shown to be inconsistent.
We prove that PTC
(n) (the polynomial time closure of the nonstandard natural number n in the model N of S
2.) cannot be a model of U
2. This implies that there exists a first order sentence of bounded arithmetic which is provable in U
2 but does not hold in PTC
The relativized propositional calculus is a system of Boolean formulas with query symbols. A formula in this system is called a one-query formula if the number of occurrences of query symbols is just one. If a one-query formula is a tautology with respect to a given oracle A then it is called a...
In this paper, we develop primitive recursive analogues of regular cardinals by using ordinal representation systems for KPi and KPM. We also define primitive recursive analogues of inaccessible and hyperinaccessible cardinals. Moreover, we characterize the primitive recursive analogue of the...
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