5. A set of formulas Mo is an axiom system for a set of formulas M if {A A is a model for Mo} = {A | A is a model for M} M is called finitely axiomatizable if it has a finite axiom system. Suppose {F1, F2, F3,...} is an axiom system for a set M where for all n ≥ 1, Fn+1 → Fn and Fn → Fn+1. Show that M is not finitely axiomatizable.

Question

This question is from course Advanced Logic in graduate level. Please give the answer, if yoy know, in a clear and understandable way, as soon as you can.

Answer 1

Expert Solution

Answer 2

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution

See solution Check out a sample Q&A here

Step 1: Given

VIEW

Step 2: Proof

VIEW

Solution

VIEW

Answer 3

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution

See solution Check out a sample Q&A here

Answer 4

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution

Answer 5

This question has been solved!

Answer 6

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

Answer 7

This is a popular solution

Answer 8

This is a popular solution

Answer 9

See solution Check out a sample Q&A here

Answer 10

Trending nowThis is a popular solution!

Step by stepSolved in 3 steps

See solution

Check out a sample Q&A here

Answer 11

Trending nowThis is a popular solution!

Step by stepSolved in 3 steps

See solution

Check out a sample Q&A here

Answer 12

Trending nowThis is a popular solution!

Step by stepSolved in 3 steps

Answer 13

Trending nowThis is a popular solution!

Answer 14

Trending nowThis is a popular solution!

Answer 15

Trending now

Answer 16

This is a popular solution!

Answer 17

Step by stepSolved in 3 steps

Answer 18

Step by stepSolved in 3 steps

Answer 19

Step by step

Answer 20

Solved in 3 steps

Answer 21

See solution

Check out a sample Q&A here

Answer 22

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

in the solution it says "Now, consider the model that satisfies all axioms in {A1, A2, ..., Ak} (since it's finite, it can be satisfied by a model), but also satisfies Fm because Fm implies Fm+1" but it is given that Fm doesnot imply fm+1

Solution

by Bartleby Expert

SEE SOLUTION

Answer 23

Read through expert solutions to related follow-up questions below.

Follow-up Question

in the solution it says "Now, consider the model that satisfies all axioms in {A1, A2, ..., Ak} (since it's finite, it can be satisfied by a model), but also satisfies Fm because Fm implies Fm+1" but it is given that Fm doesnot imply fm+1

Solution

by Bartleby Expert

SEE SOLUTION

Answer 24

Read through expert solutions to related follow-up questions below.

Answer 25

Follow-up Question

in the solution it says "Now, consider the model that satisfies all axioms in {A1, A2, ..., Ak} (since it's finite, it can be satisfied by a model), but also satisfies Fm because Fm implies Fm+1" but it is given that Fm doesnot imply fm+1

Solution

by Bartleby Expert

SEE SOLUTION

Answer 26

Follow-up Question

in the solution it says "Now, consider the model that satisfies all axioms in {A1, A2, ..., Ak} (since it's finite, it can be satisfied by a model), but also satisfies Fm because Fm implies Fm+1" but it is given that Fm doesnot imply fm+1

Solution

by Bartleby Expert

SEE SOLUTION

Answer 27

Follow-up Question

in the solution it says "Now, consider the model that satisfies all axioms in {A1, A2, ..., Ak} (since it's finite, it can be satisfied by a model), but also satisfies Fm because Fm implies Fm+1" but it is given that Fm doesnot imply fm+1

Answer 28

Follow-up Question

Answer 29

Follow-up Question

Answer 30

in the solution it says "Now, consider the model that satisfies all axioms in {A1, A2, ..., Ak} (since it's finite, it can be satisfied by a model), but also satisfies Fm because Fm implies Fm+1" but it is given that Fm doesnot imply fm+1

Answer 31

in the solution it says "Now, consider the model that satisfies all axioms in {A1, A2, ..., Ak} (since it's finite, it can be satisfied by a model), but also satisfies Fm because Fm implies Fm+1" but it is given that Fm doesnot imply fm+1

Answer 32

Solution

by Bartleby Expert

SEE SOLUTION

Answer 33

Solution

by Bartleby Expert

SEE SOLUTION

Answer 34

Solution

by Bartleby Expert

Answer 35

by Bartleby Expert

Answer 36

by Bartleby Expert

Answer 37

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

in the solution it says "Now, consider the model that satisfies all axioms in {A1, A2, ..., Ak} (since it's finite, it can be satisfied by a model), but also satisfies Fm because Fm implies Fm+1" but it is given that Fm doesnot imply fm+1

Solution

by Bartleby Expert

SEE SOLUTION

Answer 38

Read through expert solutions to related follow-up questions below.

Follow-up Question

in the solution it says "Now, consider the model that satisfies all axioms in {A1, A2, ..., Ak} (since it's finite, it can be satisfied by a model), but also satisfies Fm because Fm implies Fm+1" but it is given that Fm doesnot imply fm+1

Solution

by Bartleby Expert

SEE SOLUTION

Answer 39

Read through expert solutions to related follow-up questions below.

Answer 40

Follow-up Question

in the solution it says "Now, consider the model that satisfies all axioms in {A1, A2, ..., Ak} (since it's finite, it can be satisfied by a model), but also satisfies Fm because Fm implies Fm+1" but it is given that Fm doesnot imply fm+1

Solution

by Bartleby Expert

SEE SOLUTION

Answer 41

Follow-up Question

in the solution it says "Now, consider the model that satisfies all axioms in {A1, A2, ..., Ak} (since it's finite, it can be satisfied by a model), but also satisfies Fm because Fm implies Fm+1" but it is given that Fm doesnot imply fm+1

Solution

by Bartleby Expert

SEE SOLUTION

Answer 42

Follow-up Question

in the solution it says "Now, consider the model that satisfies all axioms in {A1, A2, ..., Ak} (since it's finite, it can be satisfied by a model), but also satisfies Fm because Fm implies Fm+1" but it is given that Fm doesnot imply fm+1

Answer 43

Follow-up Question

Answer 44

Follow-up Question

Answer 45

in the solution it says "Now, consider the model that satisfies all axioms in {A1, A2, ..., Ak} (since it's finite, it can be satisfied by a model), but also satisfies Fm because Fm implies Fm+1" but it is given that Fm doesnot imply fm+1

Answer 46

in the solution it says "Now, consider the model that satisfies all axioms in {A1, A2, ..., Ak} (since it's finite, it can be satisfied by a model), but also satisfies Fm because Fm implies Fm+1" but it is given that Fm doesnot imply fm+1

Answer 47

Solution

by Bartleby Expert

SEE SOLUTION

Answer 48

Solution

by Bartleby Expert

SEE SOLUTION

Answer 49

Solution

by Bartleby Expert

Answer 50

by Bartleby Expert

Answer 51

by Bartleby Expert

Related questions