## Algorithmic Properties of Structures: Selected Papers of Erwin EngelerThe work of Erwin Engeler in the logic and algebra of computer science has been influential but has become difficult to access because it has appeared in different types of publications. This collection of selected papers is therefore timely and useful. It represents an original and coherent approach to the basic interrelationships between mathematics and computer science.The volume begins with the area of enrichment of classical model theory by languages which express properties representing the outcome of hypothetical computer programs executed in a given class of mathematical structures, and is related to questions of correctness and provability of programs. This point of view allowed the generalization of classical Galois theory to the point of discussing the relation between structure and complexity of solution programs for problems posed in various mathematical theories. The algebraic approach is deepened and enlarged in the later papers by showing that the algorithmic aspects of any mathematical structure can be uniformly dealt with by expanding these structures into combinatory algebras. |

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### Contents

Logics of Algorithmic Properties | 1 |

Syntax | 31 |

Vol 72 Springer 1968 6476 31 | 49 |

Symp Auto | 62 |

Symp Semantics | 73 |

Mathem Logic in Com | 87 |

Intern Symp on Theoretical Program | 97 |

Galois Theory and the Structure of Problems | 107 |

Math Found | 131 |

Structural relations between programs and problems Int Congr | 137 |

An Algebraization of Algorithmics | 183 |

### Common terms and phrases

algebraic structure algorithmic basis algorithmic formulas algorithmic problems algorithmic properties amalgamation property approximates atomic formulas automorphism auxiliary problems axiomatic axioms basic binary operation Boolean combinatory algebra combinatory differential fields combinatory logic conditional instruction consider consistent construction Corollary corresponding defined definition denote differential field elements Engeler equivalent example exit expression extension F U A F U A(x first-order fixpoint formal Galois group Galois theory geometry given go to q graph algebra induction input isomorphic label Lambda Calculus Lemma Let F logic programs lower bounds m-expressions machines Math mathematical minimal model natural numbers normal form notion obtained obvious ordered field partial function permutation predicate processes program TT programming language proof theory quantifier-free real numbers recursive relational structure result satisfy sequence set of formulas signature simple programs solvability solving splitting diagram subsets of G(A symbols Theorem universal theory variables well-posed well-posed problem