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Shelah's creature forcing is a very powerful method, with wide range of applications. The method also has some applications in ZFC, let's quote a few of them that I am aware of:

(1) In A partition theorem Shelah proves a very general infinitary Ramsey theorem in ZFC, which is parallel to the Galvin-Prikry theorem and the Carlson-Simpson theorem.

(2) In Partition theorems from creatures and idempotent ultrafilters, creature forcing is used to prove some Ramsey type theorems. As an application of their general method, new proof of Carlson-Simpson theorem is given. See also Creature forcing and topological Ramsey spaces

(3) In Ramsey theorems for product of finite sets with submeasures creature forcing is used to prove a parametrized partition theorem on products of finite sets equipped with submeasures. It improves the results of DiPrisco, Llopis, and Todorcevic.

Question 1. What other ZFC examples are available whose proofs is given by creature forcing?

Question 2. Are there any applications of creature forcing in proving ZFC results, beyond those in Ramsey type theorems?

Shelah's creature forcing is a very powerful method, with wide range of applications. The method also has some applications in ZFC, let's quote a few of them that I am aware of:

(1) In A partition theorem Shelah proves a very general infinitary Ramsey theorem in ZFC, which is parallel to the Galvin-Prikry theorem and the Carlson-Simpson theorem.

(2) In Partition theorems from creatures and idempotent ultrafilters, creature forcing is used to prove some Ramsey type theorems. As an application of their general method, new proof of Carlson-Simpson theorem is given. See also Creature forcing and topological Ramsey spaces

(3) In Ramsey theorems for product of finite sets with submeasures creature forcing is used to prove a parametrized partition theorem on products of finite sets equipped with submeasures. It improves the results of DiPrisco, Llopis, and Todorcevic.

Question 1. What other ZFC examples are available whose proofs is given by creature forcing?

Question 2. Are there any applications of creature forcing in proving ZFC results, beyond those in Ramsey type theorems?

Shelah's creature forcing is a very powerful method, with wide range of applications. The method also has some applications in ZFC, let's quote a few of them that I am aware of:

(1) In A partition theorem Shelah proves a very general infinitary Ramsey theorem in ZFC, which is parallel to the Galvin-Prikry theorem and the Carlson-Simpson theorem.

(2) In Partition theorems from creatures and idempotent ultrafilters, creature forcing is used to prove some Ramsey type theorems. As an application of their general method, new proof of Carlson-Simpson theorem is given. See also Creature forcing and topological Ramsey spaces

(3) In Ramsey theorems for product of finite sets with submeasures creature forcing is used to prove a parametrized partition theorem on products of finite sets equipped with submeasures. It improves the results of DiPrisco, Llopis, and Todorcevic.

Question 1. What other ZFC examples are available whose proofs is given by creature forcing?

 

Question 2. Are there any applications of creature forcing in proving ZFC results, beyond those in Ramsey type theorems?

Shelah's creature forcing is a very powerful method, with wide range of applications. The method also has some applications in ZFC, let's quote a few of them that I am aware of:

(1) In A partition theorem Shelah proves a very general infinitary Ramsey theorem in ZFC, which is parallel to the Galvin-Prikry theorem and the Carlson-Simpson theorem.

(2) In Partition theorems from creatures and idempotent ultrafilters, creature forcing is used to prove some Ramsey type theorems. As an application of their general method, new proof of Carlson-Simpson theorem is given. See also Creature forcing and topological Ramsey spaces

(3) In Ramsey theorems for product of finite sets with submeasures creature forcing is used to prove a parametrized partition theorem on products of finite sets equipped with submeasures. It improves the results of DiPrisco, Llopis, and Todorcevic.

Question 1. What other ZFC examples are available whose proofs is given by creature forcing?

Question 2. Are there any applications of creature forcing in proving ZFC results, beyond those in Ramsey type theorems?

Shelah's creature forcing is a very powerful method, with wide range of applications. The method also has some applications in ZFC, let's quote a few of them that I am aware of:

(1) In A partition theorem Shelah proves a very general infinitary Ramsey theorem in ZFC, which is parallel to the Galvin Prikry theorem and the Carlson-Sympson theorem.

(2) In Partition theorems from creatures and idempotent ultrafilters, creature forcing is used to prove some Ramsey type theorems. As an application of their general method, new proof of Carlson-Sympson theorem is given. See also Creature forcing and topological Ramsey spaces

(3) In Ramsey theorems for product of finite sets with submeasures creature forcing is used to prove a parametrized partition theorem on products of finite sets equipped with submeasures. It improves the results of DiPrisco, Llopis, and Todorcevic.

Question 1. What other ZFC examples are available whose proofs is given by creature forcing?

Question 2. Are there any applications of creature forcing in proving ZFC results, beyond those in Ramsey type theorems?

Shelah's creature forcing is a very powerful method, with wide range of applications. The method also has some applications in ZFC, let's quote a few of them that I am aware of:

(1) In A partition theorem Shelah proves a very general infinitary Ramsey theorem in ZFC, which is parallel to the Galvin-Prikry theorem and the Carlson-Simpson theorem.

(2) In Partition theorems from creatures and idempotent ultrafilters, creature forcing is used to prove some Ramsey type theorems. As an application of their general method, new proof of Carlson-Simpson theorem is given. See also Creature forcing and topological Ramsey spaces

(3) In Ramsey theorems for product of finite sets with submeasures creature forcing is used to prove a parametrized partition theorem on products of finite sets equipped with submeasures. It improves the results of DiPrisco, Llopis, and Todorcevic.

Question 1. What other ZFC examples are available whose proofs is given by creature forcing?

Question 2. Are there any applications of creature forcing in proving ZFC results, beyond those in Ramsey type theorems?