Kolmogorov complexity and set theoretical representations of integers

We reconsider some classical natural semantics of integers (namely iterators of functions, cardinals of sets, index of equivalence relations) in the perspective of Kolmogorov complexity. To each such semantics one can attach a simple representation of integers that we suitably effectivize in order to develop an associated Kolmogorov theory. Such effectivizations are particular instances of a ge...

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Church, Cardinal and Ordinal Representations of Integers and Kolmogorov complexity

We consider classical representations of integers: Church’s function iterators, cardinal equivalence classes of sets, ordinal equivalence classes of totally ordered sets. Since programs do not work on abstract entities and require formal representations of objects, we effectivize these abstract notions in order to allow them to be computed by programs. To any such effectivized representation is...

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Set theoretical Representations of Integers, I

We reconsider some classical natural semantics of integers (namely iterators of functions, cardinals of sets, index of equivalence relations) in the perspective of Kolmogorov complexity. To each such semantics one can attach a simple representation of integers that we suitably effectivize in order to develop an associated Kolmogorov theory. Such effectivizations are particular instances of a ge...

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2 J an 2 00 8 Church , Cardinal and Ordinal Representations of Integers and Kolmogorov complexity

We consider classical representations of integers: Church’s function iterators, cardinal equivalence classes of sets, ordinal equivalence classes of totally ordered sets. Since programs do not work on abstract entities and require formal representations of objects, we effectivize these abstract notions in order to allow them to be computed by programs. To any such effectivized representation is...

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compactifications and representations of transformation semigroups

this thesis deals essentially (but not from all aspects) with the extension of the notion of semigroup compactification and the construction of a general theory of semitopological nonaffine (affine) transformation semigroup compactifications. it determines those compactification which are universal with respect to some algebric or topological properties. as an application of the theory, it is i...

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Kolmogorov complexity and set theoretical representations of integers

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