Basic First Order Logic

• A logical symbol

• An optional symbol

• Neither

• "And"

• "Or"

• "Implies"

• "For all"

• "There exists"

What is a structure of a first order language?

• A set with interpretations of the logical symbols.

• The rules for logical deduction.

• A set with interpretations of the optional symbols.

• A set with interpretations of all the symbols in the language.

• A set of syntactical rules for forming terms and formulae of the language.

Given the language L consisting of a binary relation symbol R(-,-), a unary function symbol f(-), and two constants c and d, which of the following is a well-defined L-term?

• R(x,f(x))

• f(x)=c

• f(c)

• )f(

• g(x)

Given the language L consisting of a binary relation symbol R(-,-), a unary function symbol f(-) and two constants c and d, which of the following is a well-defined L-formula?

• R(x,f(x))

• Yes

• No

Fill in the gap:

A map between two structures is an embedding if it preserves all ___________ formulae.

What makes an embedding an elementary embedding.