MHB Logic Book: Definitions, Language & Existential Formulas

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A user seeks recommendations for a logic book that includes definitions of concepts such as language and positive existential formulas. Another participant suggests "Logic, Language, and Meaning, Volume 1: Introduction to Logic" by Gamut as a potential resource. The discussion emphasizes the need for clarity in definitions within logic studies. Participants are encouraged to share additional suggestions if they know of other relevant texts. The conversation highlights the importance of foundational knowledge in logic.
mathmari
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Hey! :o

Could you suggest a book of logic that contains definitions, like the definition of a language, of an (positive) existential formula, etc?
 
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Thread 'Hypothesis testing: Defining H0, HA hypotheses so that ( H_A)_A' makes sense'

The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...
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