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A non-uniform finitary relational semantics of system T

Lionel Vaux (2013)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We study iteration and recursion operators in the denotational semantics of typed λ-calculi derived from the multiset relational model of linear logic. Although these operators are defined as fixpoints of typed functionals, we prove them finitary in the sense of Ehrhard’s finiteness spaces.

Embedding lattices in the Kleene degrees

Hisato Muraki (1999)

Fundamenta Mathematicae

Under ZFC+CH, we prove that some lattices whose cardinalities do not exceed 1 can be embedded in some local structures of Kleene degrees.

Hierarchies of function classes defined by the first-value operator

Armin Hemmerling (2008)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

The first-value operator assigns to any sequence of partial functions of the same type a new such function. Its domain is the union of the domains of the sequence functions, and its value at any point is just the value of the first function in the sequence which is defined at that point. In this paper, the first-value operator is applied to establish hierarchies of classes of functions under various settings. For effective sequences of computable discrete functions, we obtain a hierarchy connected...

Hierarchies of function classes defined by the first-value operator

Armin Hemmerling (2007)

RAIRO - Theoretical Informatics and Applications

The first-value operator assigns to any sequence of partial functions of the same type a new such function. Its domain is the union of the domains of the sequence functions, and its value at any point is just the value of the first function in the sequence which is defined at that point. In this paper, the first-value operator is applied to establish hierarchies of classes of functions under various settings. For effective sequences of computable discrete functions, we obtain a hierarchy connected...

Provident sets and rudimentary set forcing

A. R. D. Mathias (2015)

Fundamenta Mathematicae

Using the theory of rudimentary recursion and provident sets expounded in [MB], we give a treatment of set forcing appropriate for working over models of a theory PROVI which may plausibly claim to be the weakest set theory supporting a smooth theory of set forcing, and of which the minimal model is Jensen’s J ω . Much of the development is rudimentary or at worst given by rudimentary recursions with parameter the notion of forcing under consideration. Our development eschews the power set axiom. We...

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