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By Saul A. Basri

ISBN-10: 0444534091

ISBN-13: 9780444534095

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Extra info for A deductive theory of space and time (no TOC)

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1. Let (It : t ∈ X ) be a family of sequences and A a set of parameters. We say that the sequences (It : t ∈ X ) are mutually indiscernible over A if for each t ∈ X , the sequence It is indiscernible over A ∪ I=t . 2. Let (It : t < α) be a family of sequences and A a set of parameters. Inductively construct It realizing the EM-type of It over AIt and indiscernible over that set. Then the sequences (It : t < α) are mutually indiscernible. Proof. Fix t < α. By construction It is indiscernible over At := AI>t I

Let (M , I ) be an elementary extension of (M, I ) which is |M |+ -saturated. Then we can write I = (ai : i ∈ I ) where I ⊃ I is ordered such that i

Let M be a model containing A, I and b. Write a¯i = (ai : j < α). Let P(x) and A(x) be two new unary predicates, and E(x, y), F(x, y), R(x, y) be new binary predicates. Set L = L ∪ {P, A, E, F, R} and expand M into an L -structure (M ; P, A, E, F, R) by setting P(M ) = {aij : j < α, i ∈ I} ∪ A, A(M ) = A, E(M ) = {(aij , aij ) : i ∈ I, j, j < α}, F(M ) = {(aij , aij ) : i, i ∈ I, j < α} and R(M ) = {(aij , aij ) : i < i ∈ I, j, j < α}. 4. Shrinking of indiscernible sequences 41 Let (M ; P, A, E, F, R) ≺ (M ; P , A , E , F , R ) be some |M |+ -saturated elementary extension.

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A deductive theory of space and time (no TOC) by Saul A. Basri


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