81. Publications In Logic minimal theories II, J. Symbolic logic 37(1972 6. On universal Horn theories categoricalin some infinitepower, (with AH Lachlan), algebra Universalis (fasc http://www.math.uic.edu/~jbaldwin/pmodel.html

Publications in Logic John T. Baldwin On strongly minimal sets, (with A. H. Lachlan), J. SymbolicLogic 36 (1971), 79-96. Alpha T is finite for aleph-one categorical T, Trans.Amer. Math. Soc. 181 (1973), 37-51. Almost strongly minimal theories I, J. Symbolic Logic 37(1972), 481-493. Almost strongly minimal theories II, J. Symbolic Logic 37(1972), 657-660. The number of automorphisms of a model of an aleph-onecategorical theory, Fund. Math., (1) 83 (1973), 1-6. On universal Horn theories categorical in some infinitepower, (with A. H. Lachlan), Algebra Universalis (fasc. 1) 3 (1973),98-111. A sufficient condition for a variety to have the amalgamationproperty, Colloq. Math. (fasc. 2) XXVIII (1973), 81-83. A "natural" theory without a prime model, (with A. Blass,D.W. Kueker and A.M.W. Glass), Algebra Universalis (fasc. 2)3 (1973), 152-155. A topology for the space of countable models of a first ordertheory, (with J. M. Plotkin), Z. Math. Logik Grundlag.Math. 20 (1974) 173-178. Atomic compactness and aleph-one categorical Horntheories, Fund. Math. LXXXII (1975), 7-9. Conservative extensions and the two cardinal theoremfor stable theories, Fund. Math. LXXXVIII (1975), 7-9.

82. Www.uwm.edu/~whopkins/logic/Logic.txt Negatives; Intuitionistic vs. Classical logic (4) A categorical AlgebraFor logic (5) Sequents (6) Basic Properties The Cut Rule http://www.uwm.edu/~whopkins/logic/Logic.txt

From: whopkins@csd.uwm.edu (Alfred Einstead) Newsgroups: sci.logic Subject: A Simple Formal, Mathematical Definition Of Logic (was: Maths) References: NNTP-Posting-Host: 129.89.7.202 Message-ID: ; L = f; R = g Disjunction: h = [hS,hT]; [f,g]S = f; [f,g]T = g Implication: @ L,R> = f; > = g Failure: f[] = [] Universal: h = ; Ax = h Existential: h = [x:Ex h]; [x:h]Ex = h In addition, new identities may be formed by Substitution: f(T) = g(T) where f(x) = g(x) Here, as far as substitution is concerned, a variable y in the term [y:f], are bound and so the substitution are defined the same way as they were for the quantifier terms Ay.P and Ey.P. Technically, to make this more precise you have to index all the basic items by the propositions involved. So the actual identities would read: f I(B) = f = I(A) f, where f: A -> B h =

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