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We give a new proof showing that it is not possible to define in monadic second-order logic (MSO) a choice function on the infinite binary tree. This result was first obtained by Gurevich and Shelah using set theoretical arguments. Our proof is much simpler and only uses basic tools from automata theory. We show how the result can be used to prove the inherent ambiguity of languages of infinite trees. In a second part we strengthen the result of the non-existence of an MSO-definable well-founded...

Completeness of cut-free type theories.

Mitsuru Yasuhara (1974)

Archiv für mathematische Logik und Grundlagenforschung

Completeness properties of classical theories of finite type and the normal form theorem [Book]

Peter Päppinghaus (1983)

...-definable functionals and ... Conversion.

R. Statman (1983)

Archiv für mathematische Logik und Grundlagenforschung

Definitions: the primitive concept of logics or The Leśniewski-Tarski legacy [Book]

E. G. K. López-Escobar, Francisco Miraglia (2002)

Deux relations dénombrables, logiquement équivalentes pour le second ordre, sont isomorphes

R. Fraisse (1977)

Publications du Département de mathématiques (Lyon)

Ein starker Normalisationssatz für die intuitionistische Typentheorie.

Wolfram Pohler (1973)

Manuscripta mathematica

Enumerated type semantics for the calculus of looping sequences

Livio Bioglio (2011)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

The calculus of looping sequences is a formalism for describing the evolution of biological systems by means of term rewriting rules. In this paper we enrich this calculus with a type discipline which preserves some biological properties depending on the minimum and the maximum number of elements of some type requested by the present elements. The type system enforces these properties and typed reductions guarantee...

Enumerated type semantics for the calculus of looping sequences

Livio Bioglio (2011)

RAIRO - Theoretical Informatics and Applications

First order topology [Book]

C.W. Henson, C.G. Jockusch, Jr., L.A. Rubel, G. Takeuti (1977)

Ganzgeschlossene und prädikatgeschlossene Logiken I.

Jörg Flum (1971)

Archiv für mathematische Logik und Grundlagenforschung

Ganzgeschlossene und prädikatgeschlossene Logiken II.

Jörg Flum (1971)

Archiv für mathematische Logik und Grundlagenforschung

General operators binding variables in the interpreted modal calculus $\mathcal{MC}^{\nu}$

Aldo Bressan, Alberto Zanardo (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si considera il calcolo modale interpretato $\mathcal{MC}^{\nu}$ , che è basato su un sistema di tipi con infiniti livelli, contiene descrizioni, ed è dotato di una semantica di tipo generale - v. [2], o [3], o [4], o [5]. In modo semplice e naturale si introducono in $\mathcal{MC}^{\nu}$ operatori vincolanti variabili, di tipo generale. Per teorie basate sul calcolo logico risultante $\mathcal{MC}^{\nu}$ vale un teorema di completezza, che si dimostra in modo immediato sulla base dell'estensione del teorema parziale di completezza stabilito in [11], fatta...

Geometric and higher order logic in terms of abstract Stone duality.

Taylor, Paul (2000)

Theory and Applications of Categories [electronic only]

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