142:(The Theory of Models, North-Holland Publishing Co., 1965) as "On the denumerable models of theories with extra predicates", pp 376–389. In this paper he characterizes the countable ("denumerable") structures which can be made into models of a theory by adding interpretations of the extra predicates used in defining the theory. His characterization involves (infinite) expressions beginning with an infinite sequence of alternating quantifiers. Such expressions are now interpreted using infinite two-person games. The importance of this work was only realized after it was rediscovered and extended by Robert Vaught in his work on
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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
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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
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Presumably as a result of these papers he was named a visiting associate professor at The
University of California, Berkeley, for 1962–1963, and gave an Invited Address at the International Symposium on the Theory of Models held there in 1963. His address was published in the Conference Proceedings
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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
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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.
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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 to 1969, and was professor of philosophy at the
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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.
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Svenonius' reputation as a mathematical model theorist was established with the publication of three papers in
Theoria in 1959 and 1960:
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who defines "Svenonius games" and "Svenonius sentences" in his encyclopedic treatise Model Theory (Cambridge
University Press, 1993).
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The other two papers include a characterization of theories having only one countable model, obtained also by the Polish logician
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establishes what is still referred to as the 'Svenonius theorem' on decidability. One of his proponents in Sweden was
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Washington Post: Lars
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equivalent characterizations of omega-categorical theories
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