Recent content by pooj4

The Completeness Proof for First-Order Predicate Logic depends on if $\Phi$ is a set of consistent $\mathcal L$-formulas, then $\Phi$ is satisfiable. How is that constructed? There are a large number of Lemmas working from Machover's text Set theory, Logic and Their Limitations but I'm having...

thanks that helps

There are an infinite number of natural numbers. Why is that? Well this follows from the following facts: (i) There is at least one natural number. (ii) For each natural number there is a distinct number which is its successor, i.e., for each number $x$ there is a distinct number $y$ such that...

Trouble working through Set theory, Logic, and their Limitations by Maurice Machover. Particularly these 1. $\sigma \vDash \alpha \rightarrow \forall x\alpha$ where $x$ does not occur in a free $\alpha$ 2. $\sigma \vDash s_1 = t_1 \rightarrow ... \rightarrow s_n = t_n \rightarrow...