Π40 ⁰₄ conservation of Ramsey's theorem for pairs

Key Points

• The aim is to prove that Ramsey's theorem for pairs and two colors is a conservative extension of a specific logic formula.
• Improvement of previous results by Patey and Yokoyama
• Introduction of a new general technique for proving conservation theorems
• Focus on the first-order part of Ramsey's theorem.
• Established that Ramsey's theorem for pairs is a conservative extension
• Provided a new proof method that advances understanding in logic
• Contributed to resolving longstanding questions concerning Ramsey's theorem.