## Biographies of Women Mathematicians

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### Languages with Expressions of Infinite Length

University of Southern California, 1959

Table of Contents

- Implicatitve Models and Conjuntive Implicative Models
- Embedding Implicative Models in Conjunctive Implicative Models
- Embedding Conjunctive Implicative Models in Brouwerian Algebras

- A Formulation of Languages with WFFS of Infinite Length
- Infinitary Expressions
- Description of Languages L
_{αβ}
- Free and Bound Variables, Substitution, in L
_{αβ}

- Algebraically Complete Formalizations for Languages with WFFS of Infinite Length
- Formal Systems P
_{α}(E), F_{αβ}(E)
- An Algebraic Characterization of Provability in P
_{α}(E), F_{αβ}(E)
- An Algebraic Characterization of Provability in Systems P
_{α}(E), F_{αβ}(E) with Negation

- Semantically Complete Formalizations for Languages with WFFS of Infinite Length
- Semantically Complete Formalizations for Languages P
_{α}
- Formalizations for P
_{α} and the Theory of α-complete Boolean Algebras
- Semantically Complete Formalizations for Languages F
_{αβ}