Satan is the "god" of this world?

In Luke 4:6 Satan offers Jesus the worlds and claims that they are his to give. Paul in II Corinthians 4:4 refers to Satan as the “god” of this world. In Ephesians 2:2, he is the “prince and power of the air.” I have a couple questions: Did Satan have some sort of temporary authority over the worlds? These “worlds,” were they physical or does this refer to people. Is Satan the “god” of this world because it is fallen and sinful? because man has given him that place in their hearts? What does “prince and power of the air” mean? These questions come from a friendly argument with a godly deacon that wants to make sure his pastor is doctrinally sound on the topic of Satanology (is that a word?). Thanks for your help.

Discussion

Here are some additional passages to help amplify the topic’s consideration (bold and italics mine):

Ephesians 6:10-12
10Finally, be strong in the Lord and in his mighty power.

11Put on the full armor of God so that you can take your stand against the devil’s schemes.

12For our struggle is not against flesh and blood, but against the rulers, against the authorities, against the powers of this dark world and against the spiritual forces of evil in the heavenly realms.
John 12:31
31 Now is the time for judgment on this world; now the prince of this world will be driven out.
John 14:28-31
28”You heard me say, ‘I am going away and I am coming back to you.’ If you loved me, you would be glad that I am going to the Father, for the Father is greater than I.

29I have told you now before it happens, so that when it does happen you will believe.

30I will not speak with you much longer, for the prince of this world is coming. He has no hold on me,

31but the world must learn that I love the Father and that I do exactly what my Father has commanded me.

“Come now; let us leave.
The first question is whether or not Satan has temporary authority over the “worlds” (sic). Satan’s offer itself cannot be considered trustworthy. That is, being a liar and the father of lies he only speaks deception. That might indeed involve some element of truth but such elements are alloyed with lies, thus what Satan says is never trustworthy.

But it still must be measured for what it was. What Satan offered to our Lord was the authority God had given him with respect to this world. However, it does not reveal in that one context the extent of that authority. What we must do is examine all of Scripture to determine the nature of that authority which includes its limits.

One immediate source is Job and it is clear that Satan was required to gain permission from God to attack Job (chapter 1):
9 “Does Job fear God for nothing?” Satan replied. 10 “Have you not put a hedge around him and his household and everything he has? You have blessed the work of his hands, so that his flocks and herds are spread throughout the land. 11 But stretch out your hand and strike everything he has, and he will surely curse you to your face.”

12 The LORD said to Satan, “Very well, then, everything he has is in your hands, but on the man himself do not lay a finger.”

Then Satan went out from the presence of the LORD.
So while Satan has authority it does not supersede Divine authority. So we can know what Satan offered our Lord was an authority inferior to Divine authority, but in the mind of Satan that is irrelevant since his hope was to subvert the work of the Savior and somehow cause him to abandon the Triune plan.

Therefore the question must be understood to be limited to what authority is and is not present. And unfortunately there is not readily available in Scripture a detailed list of all the do’s and don’ts of Satan, rather we must systematically observe in Scripture, from Genesis to Revelation all of the acts and work of Satan and his demons and either directly document what they were/are allowed to do or conclude by way of observation and inference what is permitted.

Clearly we can see our Lord saying about Satan that he was coming but that he has no hold on our Savior. So again there is a limit.

And from the additional passages cited along with yours the powers and work of Satan, who is generally invisible to our eyes, is described, none the less, as the prince of this world and one whose powers and our struggles against is in heavenly realms. So we do live in this world where he is considered prince, at least prince of the air or god of this world.

What we know it cannot mean is that Satan is sovereign here on earth. Only God is. So from there we look to understand the meaning or intent of the expressions cited.

This reference to the “air” and “heavenly realms” has with it the intent of describing the spirit of this world, this fallen world, which is sin of whom Satan is the father. He, Satan, is the prince of sin, the prince of that which is fallen which is this world. Hence, to answer your question whether he is the god of this world because it is fallen or not, yet that is why. Sin, rebellion, that which opposes God is Satan’s dominion.

As well and most specifically Satan does not take the form of a physically appearing ruler as we have in our countries. He is invisible, hence the “prince and power of the air”. He rules invisibly, like the air but is quite real.

So those hearts and minds that either completely reject God or believers who have reversed their course and become enemies of God, though still saved, are visible subjects in this invisible work of Satan and his demons in the kingdom.