Question

Let ${\phi }_{eq}$be defined as in Problem 6.10. Give a model of the sentence

Short answer

Answer:

The statement is proved below.

Step-by-step solution

Turing Machine

Let us first mention ${\phi }_{eq}$.

Now consider the main statement in our question:

The statement above tells about conditions of equivalence relation and less then relation.

We will define the model $(A,R_{1\text{'}}{R}_2).$

Here, A = Any universal set

$R_1$= Equivalence Relation on A

$R_2$= Less then Relation on

Line (1): Describe Condition of Equivalence Relation.

Line (2): Describe that for all x,y if x=y means x is not less than y.

Line (3): Describe that for all x, y if x = y , then either x< y or y <x.

Line (4): Describe that for all x,y,z if x< y and y<z then x<z

Line (5): Describe that for all x there is y, where x<y