Search results for: Guido Gherardi

Items from 1 to 7 out of 7 results

article

Super-strict Implications

Guido Gherardi, Eugenio Orlandelli

Bulletin of the Section of Logic > 2021 > 50 > 1 > 1-34

This paper introduces the logics of super-strict implications, where a super-strict implication is a strengthening of C.I. Lewis' strict implication that avoids not only the paradoxes of material implication but also those of strict implication. The semantics of super-strict implications is obtained by strengthening the (normal) relational semantics for strict implication. We consider all logics of...

article

Addendum to: “The Bolzano–Weierstrass theorem is the jump of weak Kőnig's lemma” [Ann. Pure Appl. Logic 163 (6) (2012) 623–655]

Vasco Brattka, Andrea Cettolo, Guido Gherardi, Alberto Marcone, more

Annals of Pure and Applied Logic > 2017 > 168 > 8 > 1605-1608

The purpose of this addendum is to close a gap in the proof of [1, Theorem 11.2], which characterizes the computational content of the Bolzano–Weierstraß Theorem for arbitrary computable metric spaces.

chapter

Internal Computability

Guido Gherardi

Lecture Notes in Computer Science > Computation and Logic in the Real World > 348-357

We extend the notion of (TTE-)computability to nonstandard universes by the traditional method of enlarging universes through ultrafilters. In this way a nonstandard notion of effectivity is obtained.

chapter

Borel Complexity of Topological Operations on Computable Metric Spaces

Vasco Brattka, Guido Gherardi

Lecture Notes in Computer Science > Computation and Logic in the Real World > 83-97

We study the Borel complexity of topological operations on closed subsets of computable metric spaces. The investigated operations include set theoretic operations as union and intersection, but also typical topological operations such as the closure of the complement, the closure of the interior, the boundary and the derivative of a set. These operations are studied with respect to different computability...

chapter

An Analysis of the Lemmas of Urysohn and Urysohn-Tietze According to Effective Borel Measurability

Guido Gherardi

Lecture Notes in Computer Science > Logical Approaches to Computational Barriers > 199-208

In [6], K. Weihrauch studied the computational properties of the Urysohn Lemma and of the Urysohn-Tietze Lemma within the framework of the TTE-theory of computation. He proved that with respect to negative information both lemmas cannot in general define computable single valued mappings. In this paper we reconsider the same problem with respect to positive information. We show that in the case of...

article

The Bolzano–Weierstrass Theorem is the jump of Weak Kőnig’s Lemma

Vasco Brattka, Guido Gherardi, Alberto Marcone

Annals of Pure and Applied Logic > 2012 > 163 > 6 > 623-655

We classify the computational content of the Bolzano–Weierstraß Theorem and variants thereof in the Weihrauch lattice. For this purpose we first introduce the concept of a derivative or jump in this lattice and we show that it has some properties similar to the Turing jump. Using this concept we prove that the derivative of closed choice of a computable metric space is the cluster point problem of...

article

How Incomputable is the Separable Hahn-Banach Theorem?

Guido Gherardi, Alberto Marcone

Electronic Notes in Theoretical Computer Science > 2008 > 221 > Complete > 85-102

We investigate some basic connections between reverse mathematics and computable analysis. In particular, we show how to use Weak König's Lemma within the framework of computable analysis to classify incomputable functions of low complexity. By defining the multi-valued function Sep and through the definition of a natural notion of reducibility for multi-valued functions, we obtain a computational...

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INFONA - science communication portal

Search results for: Guido Gherardi

Super-strict Implications

Addendum to: “The Bolzano–Weierstrass theorem is the jump of weak Kőnig's lemma” [Ann. Pure Appl. Logic 163 (6) (2012) 623–655]

Internal Computability

Borel Complexity of Topological Operations on Computable Metric Spaces

An Analysis of the Lemmas of Urysohn and Urysohn-Tietze According to Effective Borel Measurability

The Bolzano–Weierstrass Theorem is the jump of Weak Kőnig’s Lemma

How Incomputable is the Separable Hahn-Banach Theorem?

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INFONA - science communication portal

Search results for: Guido Gherardi

Super-strict Implications

Addendum to: “The Bolzano–Weierstrass theorem is the jump of weak Kőnig's lemma” [Ann. Pure Appl. Logic 163 (6) (2012) 623–655]

Internal Computability

Borel Complexity of Topological Operations on Computable Metric Spaces

An Analysis of the Lemmas of Urysohn and Urysohn-Tietze According to Effective Borel Measurability

The Bolzano–Weierstrass Theorem is the jump of Weak Kőnig’s Lemma

How Incomputable is the Separable Hahn-Banach Theorem?

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