1. The signature of the language of arithmetic contains the following symbols: the constant symbol 0;...

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1. The signature of the language of arithmetic contains the following symbols: the constant symbol 0; • the unary function symbol s (successor'; intuitively, if a stands for a natural number n, then s(x) stands for the number n +1); • the binary function symbols + (addition) and × (multiplication). As usual, the language of arithmetic contains the equality symbol =. 2. Consider again the language of arithmetic from Question 1 and con- sider the formula y = Vxy (s(x) < y) in this language. (a) Find a model M₁ such that M = 9. (b) Find a model M₂ such that M¬4. (c) Write a formula that is true in a model if, and only if, the domain of the model consists of exactly two elements. 1. The signature of the language of arithmetic contains the following symbols: the constant symbol 0; • the unary function symbol s (successor'; intuitively, if a stands for a natural number n, then s(x) stands for the number n +1); • the binary function symbols + (addition) and × (multiplication). As usual, the language of arithmetic contains the equality symbol =. 2. Consider again the language of arithmetic from Question 1 and con- sider the formula y = Vxy (s(x) < y) in this language. (a) Find a model M₁ such that M = 9. (b) Find a model M₂ such that M¬4. (c) Write a formula that is true in a model if, and only if, the domain of the model consists of exactly two elements.

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