5 problems

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Decidability conjecture for non-hypothetical logic over Peano Arithmetic
The language and proof system of non-hypothetical logic are considered over the axioms of Peano Arithmetic, denoted by $\mathsf{PA}$ , in a purely relational language. One may also…
Conjectureopendecidability logic peano-arithmeticarXiv posted 3 days ago
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Characterization of prime models by definability of uniform truth
Prime-model conjecture. These are precisely the prime models of $\operatorname{PA}$ ; that is, the stated definability property holds exactly when $\mathcal{M}$ is a prime model of…
Conjectureopenmodel-theory peano-arithmetic truth-definabilityarXiv posted 3 days ago
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The quotient of the positive polynomial model satisfies induction with equality and inequality
Quotient-model hypothesis. The quotient structure
Conjectureopenmodel-theory peano-arithmeticarXiv posted 3 days ago
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Conservativity of the extended proof schemata formalism
Conservativity conjecture. The extended formalism is a conservative extension of arithmetic.
Conjectureopenconservative-extensions peano-arithmetic proof-theoryarXiv posted 3 days ago
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Existence of 3-o.r. models and elementary extensions of models of PA
Existence conjecture. If $M$ is a model of $\operatorname{PA}$ , then $\operatorname{Th}(M)$ has a $lambda$ -universal model $N$ of cardinality $lambda^+$ which is $3$ -o.r.; moreover…
Conjectureopenmodel-theory peano-arithmetic set-theoryarXiv posted 3 days ago

5 problems

Decidability conjecture for non-hypothetical logic over Peano Arithmetic

Characterization of prime models by definability of uniform truth

The quotient of the positive polynomial model satisfies induction with equality and inequality

Conservativity of the extended proof schemata formalism

Existence of 3-o.r. models and elementary extensions of models of PA