Welcome to our community

Be a part of something great, join today!

Proving in first order logic for some arbitrary valuations of sigma in Machover's text


New member
Nov 17, 2019
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. $\sigma \vDash s_1 = t_1 \rightarrow ... \rightarrow s_n = t_n \rightarrow fs_1...s_n=ft_1...t_n$

3. $\sigma \vDash \forall x \alpha \rightarrow \alpha(x/t)$ (appealing to the fact that generally $\alpha(x/t)^\sigma = {\alpha}^{\sigma(x/t^\sigma )})$


Well-known member
MHB Math Scholar
Jan 30, 2012
What exactly has to be done?