Lars Svenonius

Lars Svenonius (1927, Skellefteå – September 27, 2010, Silver Spring, Maryland) was a Swedish logician and philosopher.

He was a visiting professor at University of California at Berkeley in 1962-63, then held a position at the University of Chicago from 1963–69, and was professor of philosophy at the University of Maryland from 1969 to 2009. He retired in 2009, but was awarded the position of Emeritus Professor, and continued to teach courses and advise students until his death at 83 years of age.

He was the first Swedish logician to work on model theory with his dissertation Some problems in Model Theory (for which the University of Uppsala awarded him a doctorate in 1960). His early work was in formal logic, and he established a reputation for brilliance early in his career with a series of proofs, including an independent proof of equivalent characterizations of omega-categorical theories. A 1959 paper of his in Theoria establishes what is still referred to as the 'Svenonius theorem' on decidability. One of his proponents in Sweden was Per Lindström.

Lars Svenonius' early work was in the field of logic known as model theory, in which properties of the interpretations ("models") of theories are studied. This field was the object of intense study and saw great progress in the 1950s, largely due to the work of Alfred Tarski and his students at the University of California, Berkeley. At the same time it became much more mathematical, both in techniques and in the concepts used. Svenonius' work was of the modern mathematical variety.

Svenonius' reputation as a mathematical model theorist was established with the publication of three papers in Theoria in 1959 and 1960:

In particular, paper (2) contains what is now called "Svenonius' Theorem", an important result on definability of predicates in first order theories. Even the statement of this result requires mathematical model-theoretic concepts. It states that if the interpretation of a predicate in any model of a first-order theory is invariant under permutations ("automorphisms") of the model fixing the other predicates, then the interpretation of that predicate is definable in every model by a formula involving only the other predicates; furthermore only finitely many such defining formulas are required. Beth's earlier definability theorem is a consequence of Svenonius' Theorem.

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