What are the current open problems and trends in pure logic research?

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In summary, the current open problems in logic include those in model theory, proof theory, and philosophical logic. The trends in research show that researchers are paying more attention to other areas of research. There is no specific book outlining the open problems in logic, but it is suggested to look at the research interests of mathematicians, such as Pillay and Shelah, through their web pages. Honestrosewater, a researcher who specializes in logic, may also be able to provide insight through private messaging.
  • #1
MathematicalPhysicist
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what are the current open problems in logic? in model theory, proof theory and philosophical logic? and what are the trends in research? what do researchers pay more attention to?


p.s
is there any book which gives an outline on the open problems in logic?
 
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  • #2
Call me a crazy, pie in the sky thinker. But. Since there are approximately 4 people here who are research mathematicians that I can think of, none of whom are logicians, here really isn't a very good place to look. However, since most every mathematician these days has a web page listing their research interests, why not look through a few of those? Pillay has moved to Leeds, Shelah is a brilliant mathematician, just have a look around you.
 
  • #3
what do researchers pay more attention to?

Other areas of research.

Zing!
 
  • #4
i thought there's a poster called honestwater or something like that, who specialises in logic and perhaps he could answer my question.
 
  • #5
I think Honestrosewater is a woman. Haven't seen a post by her for a while. You could try to PM her.
 

1. What is pure logic?

Pure logic, also known as formal logic, is a branch of mathematics that deals with the study of reasoning, inference, and proof. It uses symbols and rules to represent and manipulate logical statements in order to determine their validity.

2. What are open problems in pure logic?

Open problems in pure logic refer to questions or issues that have yet to be solved or proven within the field. These are typically complex and challenging questions that require further research and investigation.

3. How are open problems in pure logic approached?

Open problems in pure logic are approached through various methods, such as the use of formal systems, mathematical models, and computer-aided proofs. Researchers also rely on logical axioms and principles to construct arguments and solve problems.

4. What are some examples of open problems in pure logic?

Some examples of open problems in pure logic include the Continuum Hypothesis, the P vs. NP problem, and the Riemann Hypothesis. These are long-standing and highly complex problems that have yet to be solved by mathematicians.

5. Why are open problems in pure logic important?

Open problems in pure logic are important because solving them can lead to advancements and developments in various fields, such as computer science, artificial intelligence, and philosophy. They also help push the boundaries of human knowledge and understanding of logic and reasoning.

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