Studies in Logic and the Foundations of Mathematics, 1996
... Andrea CANTINI Department of Philosophy University of Florence Florence, Italy 1996 ELSEVIER ... more ... Andrea CANTINI Department of Philosophy University of Florence Florence, Italy 1996 ELSEVIER AMSTERDAM LAUSANNE NEW YORK OXFORD SHANNON TOKYO ... logical principles" and to carry out proofs in rather weak systems (just as remarked in Kreisel 1971, p ...
This entry concentrates on the emergence of non-trivial logical themes and notions from the discu... more This entry concentrates on the emergence of non-trivial logical themes and notions from the discussion on paradoxes from the beginning of the 20th century until 1945, and attempts to assess their importance for the development of contemporary logic. Paradoxes involving vagueness, knowledge, belief, and space and time are treated in separate entries.
La pubblicazione è resa disponibile sotto le norme e i termini della licenza di deposito, secondo... more La pubblicazione è resa disponibile sotto le norme e i termini della licenza di deposito, secondo quanto stabilito dalla Policy per l'accesso aperto dell'Università degli Studi di Firenze (https://www.sba.unifi.it/upload/policy-oa-2016-1.pdf)
Is there a consistent axiomatization of a stratified form of the Tarskian hierarchy, where strati... more Is there a consistent axiomatization of a stratified form of the Tarskian hierarchy, where stratification is meant in the sense of Quine’s New Foundations \(\textsf{NF}\)? In the following we propose a system of truth and abstraction, which might be regarded as an answer to the problem.
... The proof of 7.4 is a finitary version of the previous majorization argument 5.12. ... ASPECT... more ... The proof of 7.4 is a finitary version of the previous majorization argument 5.12. ... ASPECTS OFSELF-REFERENTIAL TRUTH 25 (4) can be verified without difficulty by induction on the length of the derivation d. In order to see that ... of Philosophy, University of Helsinki), 1977, 1-32. ...
We combine a variety of constructive methods (including forcing, realizability, asymmetric interp... more We combine a variety of constructive methods (including forcing, realizability, asymmetric interpretation), to obtain consistency results concerning combinatory logic with extensionality and (forms of) the axiom of choice.
We deal with ontological problems concerning basic systems of explicit mathematics, as formalized... more We deal with ontological problems concerning basic systems of explicit mathematics, as formalized in Jäger's language of types and names. We prove a generalized inseparability lemma, which implies a form of Rice's theorem for types and a refutation of the strong power type axiom POW+. Next, we show that POW+ can already be refuted on the basis of a weak uniform comprehension without complementation, and we present suitable optimal refinements of the remaining results within the weaker theory.
The aim of this paper is to introduce a formal system STW of self-referential truth, which extend... more The aim of this paper is to introduce a formal system STW of self-referential truth, which extends the classical first-order theory of pure combinators with a truth predicate and certain approximation axioms. STW naturally embodies the mechanisms of general predicate application/abstraction on a par with function application/abstraction; in addition, it allows non-trivial constructions, inspired by generalized recursion theory. As a consequence, STW provides a smooth inner model for Myhill's systems with levels of implication.
Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 1992
ABSTRACT We investigate a theory of Frege structures extended by the Myhill-Flagg hierarchy of im... more ABSTRACT We investigate a theory of Frege structures extended by the Myhill-Flagg hierarchy of implications. We study its relation to a property theory with an approximation operator and we give a proof theoretical analysis of the basic system involved. MSC: 03F35, 03D60.
... and Philosophy of Science, Florence, August 1995 Edited by ANDREA CANTINI University of Flore... more ... and Philosophy of Science, Florence, August 1995 Edited by ANDREA CANTINI University of Florence, Italy ETTORE CASARI University of ... Low-Power Wireless Infrared Communications by Rob Otte Philips Research Leo P. de Jong Delft University of Technology and Arthur ...
Studies in Logic and the Foundations of Mathematics, 1996
... Andrea CANTINI Department of Philosophy University of Florence Florence, Italy 1996 ELSEVIER ... more ... Andrea CANTINI Department of Philosophy University of Florence Florence, Italy 1996 ELSEVIER AMSTERDAM LAUSANNE NEW YORK OXFORD SHANNON TOKYO ... logical principles" and to carry out proofs in rather weak systems (just as remarked in Kreisel 1971, p ...
This entry concentrates on the emergence of non-trivial logical themes and notions from the discu... more This entry concentrates on the emergence of non-trivial logical themes and notions from the discussion on paradoxes from the beginning of the 20th century until 1945, and attempts to assess their importance for the development of contemporary logic. Paradoxes involving vagueness, knowledge, belief, and space and time are treated in separate entries.
La pubblicazione è resa disponibile sotto le norme e i termini della licenza di deposito, secondo... more La pubblicazione è resa disponibile sotto le norme e i termini della licenza di deposito, secondo quanto stabilito dalla Policy per l'accesso aperto dell'Università degli Studi di Firenze (https://www.sba.unifi.it/upload/policy-oa-2016-1.pdf)
Is there a consistent axiomatization of a stratified form of the Tarskian hierarchy, where strati... more Is there a consistent axiomatization of a stratified form of the Tarskian hierarchy, where stratification is meant in the sense of Quine’s New Foundations \(\textsf{NF}\)? In the following we propose a system of truth and abstraction, which might be regarded as an answer to the problem.
... The proof of 7.4 is a finitary version of the previous majorization argument 5.12. ... ASPECT... more ... The proof of 7.4 is a finitary version of the previous majorization argument 5.12. ... ASPECTS OFSELF-REFERENTIAL TRUTH 25 (4) can be verified without difficulty by induction on the length of the derivation d. In order to see that ... of Philosophy, University of Helsinki), 1977, 1-32. ...
We combine a variety of constructive methods (including forcing, realizability, asymmetric interp... more We combine a variety of constructive methods (including forcing, realizability, asymmetric interpretation), to obtain consistency results concerning combinatory logic with extensionality and (forms of) the axiom of choice.
We deal with ontological problems concerning basic systems of explicit mathematics, as formalized... more We deal with ontological problems concerning basic systems of explicit mathematics, as formalized in Jäger's language of types and names. We prove a generalized inseparability lemma, which implies a form of Rice's theorem for types and a refutation of the strong power type axiom POW+. Next, we show that POW+ can already be refuted on the basis of a weak uniform comprehension without complementation, and we present suitable optimal refinements of the remaining results within the weaker theory.
The aim of this paper is to introduce a formal system STW of self-referential truth, which extend... more The aim of this paper is to introduce a formal system STW of self-referential truth, which extends the classical first-order theory of pure combinators with a truth predicate and certain approximation axioms. STW naturally embodies the mechanisms of general predicate application/abstraction on a par with function application/abstraction; in addition, it allows non-trivial constructions, inspired by generalized recursion theory. As a consequence, STW provides a smooth inner model for Myhill's systems with levels of implication.
Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 1992
ABSTRACT We investigate a theory of Frege structures extended by the Myhill-Flagg hierarchy of im... more ABSTRACT We investigate a theory of Frege structures extended by the Myhill-Flagg hierarchy of implications. We study its relation to a property theory with an approximation operator and we give a proof theoretical analysis of the basic system involved. MSC: 03F35, 03D60.
... and Philosophy of Science, Florence, August 1995 Edited by ANDREA CANTINI University of Flore... more ... and Philosophy of Science, Florence, August 1995 Edited by ANDREA CANTINI University of Florence, Italy ETTORE CASARI University of ... Low-Power Wireless Infrared Communications by Rob Otte Philips Research Leo P. de Jong Delft University of Technology and Arthur ...
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